NJSLA Algebra II Similarity, Right Triangles, and Trigonometry Practice

NJSLA Algebra II Similarity, Right Triangles, and Trigonometry. Practice it free.

Understand similarity in terms of similarity transformations; prove theorems involving similarity; define trigonometric ratios and solve problems involving right triangles. This Algebra II reporting domain maps to 4 practice skills and 8 representative questions from the playable bank.

Algebra IIG-SRT4 mapped skills

Similarity, Right Triangles, and Trigonometry skills

G.SRT.A.1-3 Similarity transformations and AA criterion

G.SRT.B.4-5 Triangle similarity and proof applications

G.SRT.C.6-8 Trigonometric ratios and right triangle applications

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

Official sources

New Jersey Department of Education - Assessment
New Jersey Department of Education - 2023 NJSLS-Mathematics
NJDOE - Statewide Assessment Testing Schedule 2026-27

8 free questions · 0/0 correct

Practice playeasy

Each exterior angle of a regular polygon measures $30^{\circ}$ . How many sides does the polygon have?

The exterior angles of any convex polygon sum to $360^{\circ}$ . For a regular polygon, $n \cdot 30^{\circ} = 360^{\circ}$ , so $n = 12$ .

Practice playeasy

In a right triangle, $\sin\alpha = \dfrac{5}{13}$ and $\tan\alpha = \dfrac{5}{12}$ . What is $\cos\alpha$ ?

$\cos\alpha = \dfrac{\sin\alpha}{\tan\alpha} = \dfrac{\dfrac{5}{13}}{\dfrac{5}{12}} = \dfrac{5}{13} \cdot \dfrac{12}{5} = \dfrac{12}{13}$ , or from the $5$ - $12$ - $13$ triangle: adjacent $12$ , hypotenuse $13$ .

Practice playeasy

A parking meter that is $5$ feet tall casts a shadow $2$ feet long. A radio antenna casts a shadow at the same time. If the antenna is $35$ feet tall, how long is its shadow, in feet?

Use $\dfrac{5}{2} = \dfrac{35}{s}$ . Cross-multiply: $5s = 70$ , so $s = 14$ feet.

Practice playeasy

In a $45$ - $45$ - $90$ triangle one leg is $12$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $12$ .

Practice playeasy

Two similar triangles have perimeters in the ratio $3 : 5$ . The shortest side of the smaller triangle is $6$ . What is the length of the shortest side of the larger triangle if corresponding sides are compared?

Similar figures have a constant scale factor between corresponding lengths. Perimeter ratio $3 : 5$ means each side of the larger triangle is $\dfrac{5}{3}$ times the matching side of the smaller. The larger shortest side is $6 \cdot \dfrac{5}{3} = 10$ .

Practice playeasy

In a right triangle, $\sin\alpha = \dfrac{7}{25}$ and $\cos\alpha = \dfrac{24}{25}$ . What is $\tan\alpha$ ?

$\tan\alpha = \dfrac{\sin\alpha}{\cos\alpha} = \dfrac{\dfrac{7}{25}}{\dfrac{24}{25}} = \dfrac{7}{25} \cdot \dfrac{25}{24} = \dfrac{7}{24}$ .

Practice playeasy

A $7$ -foot-tall basketball hoop casts a shadow $14$ feet long. At the same time, a brick chimney casts a shadow $20$ feet long. How tall is the chimney, in feet?